1. Field of the Invention
The present invention relates to an active noise control apparatus, and in particular to an active noise control apparatus for transmitting, from a loud speaker, a secondary noise (pseudo noise) synthesized so as to have the same amplitude as and the opposite phase to a primary noise (noise to be controlled) and to be suppressed small, and for canceling the controlled noise by acoustically overlapping therewith the secondary noise.
2. Description of the Related Art
FIG. 30 shows a prior art example of an active noise control apparatus of a feedforward type. In this example, after a noise flowing through a duct 200 toward an outlet on the right side is detected as a signal xj (j: sample time index) by a noise detecting microphone 201, the signal xj is assumed to change into a noise gj by the time when the signal reaches an error detecting microphone 202.
In this duration, a noise control filter 220 synthesizes a secondary noise Gj with the detected noise xj and a coefficient vector Hj from a coefficient updating circuit 240. Obviously when Gj=gj, the noise is canceled, so that an outputted noise from the outlet of the duct 200 becomes small.
The coefficient updating circuit 240 updates the coefficient of the noise control filter 220 in order that a signal Ej outputted as a sum of a secondary noise xe2x88x92Gj, to which a phase inversion is performed by multiplying xe2x80x9cxe2x88x921xe2x80x9d at a multiplier 205 and which is transmitted from a loud speaker 203, and the noise gj from the error detecting microphone 202 may become a minimum.
The secondary noise xe2x88x92Gj outputted from the loud speaker 203 feeds back to the noise detecting microphone 201 through the duct 200. At this time, a feedback control filter 210 is inserted in order to intercept the feedback path of the duct 200 leading to the noise detecting microphone 201 from the loud speaker 203 to prevent an occurrence of a howling.
Also, an error path filter 230 is a filter for simulating a characteristic of an error path leading to the coefficient updating circuit 240 from the output terminal of the multiplier 205 through the loud speaker 203 and the error detecting microphone 202, and is used for a coefficient update of the noise control filter 220.
At that time, it is necessary for the error path filter 230 to accurately simulate the error path.
From the structure of the prior art example shown in FIG. 30, it is seen that the noise gj is canceled when the coefficient of the noise control filter 220 is updated in order that the sum of the secondary noise xe2x88x92Gj, to which the phase inversion is performed at the multiplier 205 and which is transmitted from the loud speaker 203, and the noise gj, i.e. the output Ej from the error detecting microphone 202 may become a minimum. The most typical algorithm applied to the coefficient updating circuit 240 which updates the coefficient vector Hj is a Filtered-x NLMS method applying a general LMS (Least Mean Square) method, which is expressed by the following equation:                               H                      j            +            1                          =                              H            j                    +                                    μ              ⁢                              xe2x80x83                            ⁢                              E                j                            ⁢                              X                j                                                                    "LeftDoubleBracketingBar"                                  X                  j                                "RightDoubleBracketingBar"                            2                                                          Eq        .                  (          1          )                    
where, xcexc is a constant called xe2x80x9cstep gainxe2x80x9d, Ej is the output of the error detecting microphone 202, and Xj is a vector expressed by the following Eq.(2) composed of xe2x80x9cIxe2x80x9d number of elements Xj, Xjxe2x88x921, . . . Xj(Ixe2x88x921) expressed by Xj(1), Xj(2), . . . , Xj(I) and obtained by the output Xj of the error path filter 230, which simulates the characteristic of the error path leading to the coefficient updating circuit 240 from the output of the multiplier 205 through the error detecting microphone 202, being retraced up to the past Ixe2x88x921 sampling periods.
Xj=[Xj(1)Xj(1), . . . , Xj(I)]xe2x80x83xe2x80x83Eq.(2)
Also, the noise control filter 220 and the error path filter 230 are composed of a non-recursive type. In the following description, the number of taps in the filters 220 and 230 are expressed by xe2x80x9cIxe2x80x9d and xe2x80x9cMxe2x80x9d for the convenience""s sake.
Assuming the Filtered-x NLMS method is a coefficient updating algorithm, the following coefficient of the error path filter 230:
C=[C(1)C(2) . . . C(M)]xe2x80x83xe2x80x83Eq.(3)
is required to be an estimated value approximated, with a high accuracy, to the following impulse response of the error path:
C=[C(1)C(2) . . . C(M)]xe2x80x83xe2x80x83Eq.(4)
Generally, the coefficient of the error path filter 230 in FIG. 30 is fixed and the calculation thereof is performed by the arrangement of providing, before starting the active noise control of FIG. 30, a white noise generated by a white noise generation circuit 250, as shown in FIG. 31, to the loud speaker 203 and the error path filter 230, providing the outputs of the error detecting microphone 202 and the error path filter 230 to a subtracter 251, and providing the difference output to the coefficient updating circuit 240.
Obviously, the problem of such an error path filter is that the white noise is outputted from a white noise generator 130 through the loud speaker to the outside of the duct upon the calculation of the coefficient. In spite of a temporary occurrence, it is not preferable that a noise of another kind is outputted from the active noise control apparatus in that way.
It is also a problem that the coefficient thus calculated of the error path filter 230 is hereafter to be fixed upon the active noise control as shown in FIG. 30. This is natural because the change of the characteristic within the duct 200 after the calculation can be fully expected.
In fact, it is known that when the coefficient of the noise control filter 220 is updated by using the calculation result to decrease the noise at the position of the error detecting microphone 202, a reflection position of the noise moves from the outlet end of the duct 200 to the position of the error detecting microphone 202 to change the acoustic characteristic within the duct 200 so that the error path filter 230 fails to accurately simulate the above-mentioned error path.
This simulating operation with a lowered accuracy may have a bad influence on the accuracy maintenance of the coefficient of the noise control filter 220, whereby a sufficient quantity of the noise reduction can not be obtained, and besides the noise control operation becomes unstable. The fact that the acoustic characteristic within the duct changes along with the decrease of the estimation error of the coefficient of the noise control filter 220 indicates that the coefficient correction of the error path filter 230 is required to be repeatedly performed with the active noise control being kept operated.
For estimating the coefficient of the error path filter 230 during the active noise control, a method using a circuit arrangement shown in FIG. 32 is known.
Namely, the white noise generated by the white noise generation circuit 250 is added to the secondary noise xe2x88x92Gj from the multiplier 205 at an adder 252 to be outputted from the loud speaker 203, so that the coefficient of the error path filter 230 is updated in order that the output of the subtracter 251 may become a minimum by applying thereto the coefficient updating circuit 240 which is not operating or has become available by not performing (by fixing) the coefficient update of the noise control filter 220, different from the example of FIG. 30.
In this arrangement, since the coefficient of the error path filter 230 gives the impulse response of the error path whose characteristic has been changed by the noise control at the time when the output of the subtracter 251 has become a minimum, the coefficient at this time has only to be used at the circuit of FIG. 30.
However, in such a circuit arrangement, as mentioned above, the overlap of the white noise outputted from the loud speaker 203 during the active noise control indicates that the active noise control apparatus becomes a new noise source.
Furthermore, the Filtered-x NLMS method of the above-mentioned Eq.(1) used for the coefficient update of the error path filter 230 does not guarantee the stable operation of 100%.
Accordingly, this generally requires a practical compromise to lessen a step gain as much as possible and the possibility of being made unstable. However, since the setting of such a small step gain causes a problem that a noise canceling performance is deteriorated in fixed-point arithmetic, which is practically left unsolved upon adopting an inexpensive fixed-point signal processor.
In order to fundamentally solve this problem, an algorithm has only to be set up which makes the coefficient calculation of the error path filter 230 unnecessary.
For such an algorithm, has already been proposed a simultaneous perturbation type optimization technique (Kajikawa, Nomura, xe2x80x9cProposal of Active Noise Control System which Performs Update Only by Using Residual Signalxe2x80x9d, 1-4-12, 1997 Autumn Meeting of the Acoustical Society of Japan, pp.497-498).
The characteristic of this technique lies on the point that perturbation is added to the coefficient of the noise control filter 220 by using the white noise. This measure of adding the perturbation is equivalent to the overlap of the white noise with the secondary noise, which can not solve the problem of the arrangement in FIG. 30.
Also, the coefficient of the feedback control filter 210 is generally calculated before starting the active noise control by forming the circuit shown in FIG. 33. The calculation method is performed in order that the difference between the output of the feedback path leading to the noise detecting microphone 201 from the loud speaker 203 and the output of the feedback control filter 210 may become a minimum, resulting in that the feedback path is to be intercepted by the subtracter 204.
However, it is a problem that the coefficient thus calculated of the feedback control filter 210 is hereafter fixed naturally because the change of the characteristic within the duct 200 is fully expected.
Actually, it is known that when the coefficient of the noise control filter 220 is updated and the noise is canceled at the position of the error detecting microphone 202, the reflect position of the noise moves from the duct outlet to the error detecting microphone 202.
This change will vary the acoustic characteristic within the duct, so that the characteristic difference between the feedback control filter 210 and the actual feedback path is extended to deteriorate the interception performance of the feedback path.
This deterioration of the interception performance not only increases the danger of howling occurrence but also increases the estimated coefficient error of the noise control filter 220 and deteriorates the noise reduction performance. The fact that the acoustic characteristic within the duct changes according to the noise reduction quantity means that the coefficient correction of the feedback control filter 210 is required to be repeatedly performed during the active noise control.
For updating the coefficient of the feedback control filter 210 during the active noise control, a method shown in FIG. 34 is the most general. Namely, the white noise generated by the white noise generation circuit 250 is added to the secondary noise xe2x88x92Gj at the adder 251 to be transmitted from the loud speaker 203, and different from the example of FIG. 30, the coefficient of the feedback control filter 210 is updated in order that the output of the subtracter 204 may become a minimum by applying thereto the coefficient updating circuit 240 which has become available by stopping (fixing) the coefficient update of the noise control filter 220.
In this arrangement, when the output of the subtracter 204 becomes the minimum, the characteristic of the feedback path which has been changed by the noise control is simulated by the feedback control filter 210, so that the interception of the feedback path is realized.
However, the defect of this method obviously lies on that a different kind of noise (white noise) from the white noise generation circuit 250 introduced for reducing the noise is transmitted from the loud speaker 203.
The active noise control apparatus of the feedforward type is shown as an example in the above, while FIG. 35 shows a general arrangement of an active noise control apparatus of a feedback type. This active noise control apparatus reduces a noise wj [j: sample time index] to be controlled by acoustically overlapping therewith the synthesized noise gj transmitted from the loud speaker 203 at the position of the microphone 201. The status of reducing the noise is monitored by the output
ej=wj+gjxe2x80x83xe2x80x83Eq.(5)
of the microphone 201 and the coefficient updating circuit 240 updates the coefficient of the noise control filter 220 in order that an output ej may become the minimum.
It is to be noted that the error path filter 230 is one for simulating the characteristic of the error path leading to the coefficient updating circuit 240 from the output edge of the noise control filter 220 through a multiplier 221, the loud speaker 203, and the microphone 201, which is required for the coefficient update of the noise control filter 220.
In addition, when the gain of a closed circuit, formed by the feedback path leading to the microphone 201 from the loud speaker 203 and the noise control filter 220, exceeds xe2x80x9c1xe2x80x9d, howling occurs. Therefore, in order to prevent the howling, the feedback control filter 210 and an adder (subtracter) 211 are provided.
As seen from the above Eq.(5), when gj≈xe2x88x92wj, the noise wj is canceled, so that the noise near the microphone 201 becomes small.
The problem in the active noise control of the feedback type arises from the synthesized noise gj being generated based on the noise wj to be controlled. Namely, a delay is inevitable until the time when the noise wj to be controlled is transmitted to the microphone 201 as the synthesized noise gj after being received at the microphone 201, synthesized at the noise control filter 220, and inverted at a multiplier 221. Accordingly, the noise which can be controlled with this active noise control apparatus of the feedback type is limited to a periodical noise regardless of the time delay.
What should be most remarked upon designing this active noise control apparatus is that the apparatus is required to stably operate so as to prevent an opposite effect such as increasing the noise by introducing this apparatus.
As the most typical adaptive algorithm applied to the coefficient updating circuit 240 which updates the coefficient of the noise control filter 220 in the above-mentioned active noise control apparatus of the feedback type, the above-mentioned Filtered-x method is used in a modified form, in which the error path filter 230 is prepositioned for simulating the characteristic of the path leading to the output of the microphone 201 through the loud speaker 203.
Namely, if the synthesized noise gj outputted from the loud speaker 203 shown in FIG. 35 and reaching the microphone 201 is completely canceled by the output of the feedback control filter 210, the input xj of the noise control filter 220 assumes the noise wj itself. Accordingly, this input xj can be treated as a reference signal for the adaptive algorithm for updating the coefficient of the noise control filter 220.
Also, the output ej of the microphone 201 can be regarded as a difference between an output gj of an adaptive filter, added to a desired response wj through the feedback path leading to the microphone 201 from the loud speaker 203, and the desired response wj. With these two signals, the arrangement of this feedback type can be treated exactly in the same way as the above-mentioned active noise control apparatus of the feedforward type.
Namely, a coefficient Aj of the noise control filter 220 in this case is updated by the following equation:
Aj+1=Aj+xcexcejYjxe2x80x83xe2x80x83Eq.(6)
where Yj=[Yj(1)Yj(2) . . . Yj(I)]T is a signal vector in which xe2x80x9cIxe2x80x9d number of aggregation of yj, obtained by applying the error path filter 230 to the input xj of the noise control filter 220, are replaced by Yj(i)=yjxe2x88x92i+1.
In addition, xe2x80x9cIxe2x80x9d is the number of taps, and xe2x80x9cxcexcxe2x80x9d is a constant called xe2x80x9cstep gainxe2x80x9d.
Aj=[Aj(1)Aj(2) . . . Aj(I)]Txe2x80x83xe2x80x83Eq.(7)
is the coefficient of the noise control filter 220 set at the time j.
In order to stably update the coefficient of the noise control filter 220 by the Filtered-x LMS method, it is required that the impulse response of the feedback path leading to the output of the microphone 201 through the loud speaker 203 is preliminarily calculated and the result is set for the coefficients of the feedback control filter 210 and the error path filter 230.
The calculation is generally performed by forming the circuit as shown in FIG. 36 with the white noise generation circuit 250 before starting the active noise control. When the output xj of the subtracter 211 becomes a minimum in this circuit arrangement, it means that the feedback control filter 210 has been able to simulate the feedback path. Then, if the coefficient of the coefficient updating circuit 240 at that time is copied to the error path filter 230, the coefficient update of the noise control filter 220 is made possible by the Filtered-x LMS method.
The active noise control apparatus of the feedback type applying thereto this coefficient update method is often used, which is mentioned, for example, in the following reference (1):
(1) Omoto, et al. xe2x80x9cThe Behavior of an Adaptive Algorithm with Moving Primary Sourcexe2x80x94Performance of a Feedback Systemxe2x80x94xe2x80x9d 1997 Autumn Meeting of the Acoustical Society of Japan, 1-4-14, pp.501-502).
The flow of the signals in this active noise control apparatus of the feedback type is equivalently shown by the block diagram of FIG. 37, where
W(z): transfer function of noise wj,
X(z): transfer function of output xj of subtracter 211,
E(z): transfer function of output ej of microphone 201,
A(z): transfer function of noise control filter 220,
B(z): transfer function of feedback path leading to output of microphone 201 through loud speaker 203,
D(z): difference between transfer function B(z) of feedback path and transfer function B(z) of feedback control filter 210.
In FIG. 37, the coefficient of the noise control filter 220 is updated in order that the output E(z) of the microphone (subtracter) 201 may become a minimum. From FIG. 37, it is seen that the active noise control apparatus of the feedback type can be regarded as a liner predictor for the noise wj which uses the noise control filter 220 as the adaptive filter. As a method proposed by paying attention to this point, an active noise control of an adaptive prediction type exists, which is shown in the following reference (2):
(2) Hamada, et al. xe2x80x9cActive Noise Control Using Adaptive Prediction-Implementation by Adaptive Filterxe2x80x94xe2x80x9d 1992 Autumn Meeting of the Acoustical Society of Japan, 2-4-1, pp.531-532.
The structure controls the filter coefficient of the noise control filter 220 by using an adaptive prediction filter 223 as shown in FIG. 38. Furthermore, the linear prediction analysis portion of this active noise control of the adaptive prediction type would be shown by the block diagram, as shown in FIG. 39, where a(z) is a transfer function of the adaptive prediction filter 223.
In order to effectively operate the arrangement of this reference (2), in the same way as the reference (1) described before, it is premised that the feedback path is simulated by the feedback control filter 210 with a high accuracy, and the approximation of D(z)≈0 is realized.
Namely, when                               1                      1            -                                          D                ⁡                                  (                  z                  )                                            ⁢                              A                ⁡                                  (                  z                  )                                                                    ≈        1                            Eq        .                  xe2x80x83                ⁢                  (          8          )                    
is realized, the output X(z) of the subtracter 211 assumes the noise W(z) itself.
Furthermore, since the approximation is also B(z)={circumflex over (B)}(z), it is seen that the arrangements of FIGS. 39 and 37 form a linear prediction analysis circuit for the noise W(z) having the same structure, if these two approximations of D(z)=0 and B(z)={circumflex over (B)}(z) are applied to the circuit arrangement of FIG. 37 to exchange the connection order of the transfer function A(z) of the noise control filter 220 and the transfer function B(z) of the feedback path.
Namely, as the result of the linear prediction analysis by the circuit arrangement of FIG. 39, when the output of a subtracter 222 becomes a minimum, the coefficient of the adaptive prediction filter 223 provides the coefficient of the noise control filter 220 which minimizes the output E(z) of the microphone 201. Accordingly, when the coefficient of the adaptive prediction filter 223 is copied for the coefficient of the noise control filter 220, the noise wj is suppressed small.
However, the problem in this case is that the control principles of the active noise control apparatuses of the feedback type in FIGS. 35 and 38 both premise B(z)={circumflex over (B)}(z).
Generally, in the estimate of the impulse response of the feedback path the error is inevitable, so that it is fully expected that the response changes with time. However, it is possible to take a measure that the coefficient of the feedback control filter 210 is updated all the time to maintain B(z)={circumflex over (B)}(z) by overlapping the white noise with the synthesized noise to make it a reference signal. However, feeding the white noise to the secondary source is equal to making the active noise control apparatus a new noise source.
In the active noise control apparatus of FIG. 35, as another defect, xe2x80x9ccoefficient updating algorithm of Filtered-x type represented by Filtered-x LMS method is unstable in principlexe2x80x9d can be mentioned.
The stability condition of the Filtered-x LMS method is studied in the following reference (3):
(3) Yabuki, et al. xe2x80x9cStability Condition in Filtered-x LMS Method in case that Modeled Error Exists in C Filterxe2x80x9d The institute of electronics, information and communication engineers, (A), vol J80-A no.11, pp.1868-1876 (1997-11).
However, as a result, measures except xe2x80x9cproviding smallest step gainxe2x80x9d are not mentioned. Also, according to the analysis, even if the step gain is made small, the stability can not be completely guaranteed.
It is accordingly an object of the present invention to provide an active noise control apparatus for updating a coefficient of a noise control filter which synthesizes a secondary noise having a same amplitude as and an opposite phase to a noise to be suppressed, in which an algorithm not requiring a coefficient calculation of an error path filter without outputting a white noise from a loud speaker is set up, thereby fundamentally solving the problem of Filtered-x LMS method.
Furthermore, it is an object of the present invention to provide an active noise control apparatus which has a function of correcting a coefficient of a feedback control filter all the time corresponding to a changing impulse response of a feedback path without outputting the white noise from the loud speaker during the noise control.
Moreover, it is an object of the present invention to provide an active noise control apparatus of a feedback type having a feedback control filter which simulates a characteristic of a feedback path leading to a noise detecting microphone connected to an input of a noise control filter for synthesizing a secondary noise, through a loud speaker which transmits the secondary noise having the same amplitude as and the opposite phase to a primary noise for suppression, and which realizes an updating circuit of an essentially stable coefficient for the noise control filter without outputting the white noise from the loud speaker.
FIG. 1 shows a principle of an active noise control apparatus according to the present invention [1], and in particular is a diagram for illustrating a calculation principle of a coefficient of a noise control filter not requiring a coefficient estimation of an error path filter used for the active noise control apparatus.
In the present invention, the noise control filter comprises a first and a second noise control filter 144 and 142 respectively having a first and a second arbitrary coefficient A1 and A2, and the apparatus further comprises a first and a second overall system filter 141 and 143 which form an overall system filter for simulating a characteristic of an overall system leading to an error detecting microphone from a noise detecting microphone that detects a noise component required for synthesizing the secondary noise, and which has a first and a second coefficient S1 and S2 respectively obtained for the second and the first coefficient A1 and A2, a differential overall system filter 146 for outputting a response difference of the first and the second overall system filter 141 and 143, and an estimating noise transfer system filter 147, having a variable coefficient, connected to the differential overall system filter 146 in cascade, a white noise generated by a white noise generation circuit 250 being applied to the differential overall system filter 146 and to respective cascade combinations of the first overall system filter 141 and the second noise control filter 142, and the second overall system filter 143 and the first noise control filter 144; the coefficient of the estimating noise transfer system filter 147 being updated in order that a difference between the output of the differential overall system filter 146 and a differential output between the first and the second noise control filter 144 and 142 becomes a minimum, and the coefficient of the estimating noise transfer system filter 147 obtained at a time when the difference becomes the minimum being provided as the coefficients of the noise control filters.
In order to briefly explain the principle, the active noise control apparatus of FIG. 30 is shown by a functional block diagram as shown in FIG. 2. However, since the subtraction of the noise by the secondary noise is performed within a space of the duct 200 in FIG. 2, a subtracter 206 shown in FIG. 2 is not formed as an actual circuit. Also, being not related to the principle, the feedback control filter 210 is omitted in FIG. 2.
Also, the basic arrangement of the active noise control apparatus when the arrangement of FIG. 2 is applied to the present invention is shown in FIG. 3, wherein it is characterized that an overall system filter 260 for simulating the overall characteristic of the control system leading to the error detecting microphone 202 from the noise detecting microphone 201 is added.
Since the coefficient of the noise control filter 220 is arbitrarily set, the first and the second noise control filter 144 and 142 forming the noise control filter 220 shown in FIG. 3 are set to have a first and a second coefficient A1 and A2 so that the transfer functions are made to have the coefficients A1 and A2 by modifying the coefficient to the extent of the noise reduction quantity being not deteriorated greatly.
In addition, the first and the second coefficient S1 and S2 of the overall system filter 260, which makes an output of a subtracter 261 a minimum for the first and the second coefficient A1 and A2 set in the noise control filter 220 in the arrangement of FIG. 3, are set in the first and second overall system filter 141 and 143 shown in FIG. 1.
The differential overall system filter 146 is one for generating a difference output S1xe2x88x92S2 between the first and the second overall system filter 141 and 143. The estimating noise transfer system filter 147 is an adaptive filter for updating the coefficient in order that the output of a subtracter 148 may become a minimum by the coefficient updating circuit 240 applied from the active noise control apparatus of FIG. 3 by using a signal obtained by applying the output of the white noise generation circuit 250 to the first and the second overall system filter 141 and 143 and the differential overall system filter 146, thereby extracting the impulse response of the noise transfer system as a coefficient, included in the first and the second overall system filter 141 and 143, and the first and the second noise control filter 142 and 144.
The calculation of the coefficient of the overall system filter 260 shown in FIG. 3 is performed by temporarily stopping the coefficient update of the noise control filter 220 and applying thereto the coefficient updating circuit 240 which has become unnecessary by the stoppage. Expressing the transfer functions of the circuit shown in FIG. 3 respectively as follows:
D: transfer function of noise transfer system 200,
A: transfer function of noise control filter 220,
S: transfer function of overall system filter 260,
C: transfer function of error path 190,
the relationship of the following equation is obtained when the output of the subtracter 261 becomes the minimum:
S≈(Dxe2x88x92A)Cxe2x80x83xe2x80x83Eq.(9)
It is of course that since the coefficients of the noise control filter 220 can be arbitrarily set, the coefficients are set in order that the transfer functions may assume A1 and A2 by modifying the coefficients to the extent of the noise reduction quantity being deteriorated greatly, and the coefficients of the overall system filter 260 are updated in order that the output of the subtracter 261 may become the minimum for both coefficients.
When the output of the subtracter 261 has become the minimum by the coefficient update, the transfer functions S1 and S2 of the overall system filter 260 satisfy the following equations:
S1≈(Dxe2x88x92A1)Cxe2x80x83xe2x80x83Eq.(10)
S2≈(Dxe2x88x92A2)Cxe2x80x83xe2x80x83Eq.(11)
Obviously, with the difference between the above-mentioned both transfer functions S1 and S2, the transfer function D of the noise transfer system 200 is eliminated, so that the transfer function of the error path to be determined, i.e. the coefficient of the error path filter 230 is calculated by the following equation:
C≈(S1xe2x88x92S2)/(A2xe2x88x92A1)xe2x80x83xe2x80x83Eq.(12)
From the first and the second Eqs.(10) and (11) of the simultaneous equations, it is seen that the transfer function D of the noise transfer system 200 is included as another unknown number. If xe2x80x9cDxe2x80x9d is solved with Eqs.(10) and (11), the following equation can be obtained:
D=(S1A2xe2x88x92S2A1)/(S1xe2x88x92S2)xe2x80x83xe2x80x83Eq.(13)
Then, the transfer function of the left side of Eq.(13) has only to be converted into the impulse response. The sampled values of the impulse response assume the coefficient of the noise control filter 220 to be determined.
Namely, by taking advantage of a coefficient of a non-recursive filter corresponding to the impulse response, the characteristics of the systems are modified by the impulse response from the transfer function. Firstly, the impulse response in the noise transfer system 200 is expressed as in the following equation:
D=[D(1)D(2) . . . D(I)]xe2x80x83xe2x80x83Eq.(14)
The coefficients corresponding to the transfer functions S1 and S2 of the overall system filter 260 are respectively expressed as follows:
S1=[S1(1)S1(2) . . . S1(L)]xe2x80x83xe2x80x83Eq.(15)
S2=[S2(1)S1(2) . . . S2(L)]xe2x80x83xe2x80x83Eq.(16)
Also, two coefficients of the noise control filter 220 are expressed as follows:
A1=[A1(1)A1(2) . . . A1(I)]xe2x80x83xe2x80x83Eq.(17)
A2=[A2(1)A2(2) . . . A2(I)]xe2x80x83xe2x80x83Eq.(18)
If S1 is provided to the first overall system filter 141 of the circuit shown in FIG. 1, S2 to the second overall system filter 143, and similarly the coefficients A1 and A2 are respectively provided to the first and the second noise control filter 144 and 142 by using the above-mentioned equations, the output of a subtracter 145 assumes a response whose transfer function is S1A2xe2x88x92S2A1.
Accordingly, if the estimating noise transfer system filter 147 having a variable coefficient is connected to the differential overall system filter 146 in cascade whose filter coefficient is S1xe2x88x92S2 with the system whose transfer function S1A2xe2x88x92S2A1 being made an unknown system, and the coefficient of the estimating noise transfer system 147 is updated at the coefficient updating circuit 240 in order that the output of the subtracter 148 may become the minimum, the coefficient converges into the impulse response of the noise transfer system 200.
It is to be noted that only upon the activation preliminarily stored coefficients may be used for the first and the second coefficient respectively of the above-mentioned first and the second noise control filter, and after the activation a coefficient obtained upon the present coefficient update may be substituted for one of the first and the second coefficient, and furthermore, coefficients obtained upon the last and the present coefficient update may be provided for the first and the second coefficient.
Also, when the output of the overall system filter becomes equal to or less than a threshold value, it is preferable that the coefficient update is stopped.
FIG. 4 is a principle diagram of an active noise control apparatus according to the present invention [2]. An inverse filter composing circuit 110 forms a filter having a characteristic including a transfer function opposite to a closed circuit starting from the noise control filter 220 and returning to the noise control filter 220 again through both (parallel circuit) of the feedback path and the feedback control filter 210, the transfer function expressing a generation process of the primary noise.
A system identification circuit 120 provides two pairs of different fixed coefficients either to the feedback control filter 210 or the noise control filter 220 to update a coefficient of an adaptive filter 150 in order that a difference becomes a minimum between an output of a first filter 130 forming a numerator of a solution obtained by eliminating a transfer function component expressing the generation process of the primary noise, from simultaneous equations based on two transfer functions of an inverse filter formed within the inverse filter composing circuit 110 for the two pairs of coefficients and an output of the adaptive filter 150 connected to a second filter 140 in cascade forming a denominator of the solution.
A coefficient of the feedback control filter 210 is updated by using the coefficient of the adaptive filter 150 obtained by operating the system identification circuit 120.
The principle of the present invention is an improvement of an active noise control apparatus of the Japanese Patent Application No.9-239776 (Japanese Patent Publication Laid-open No.11-85165) by the inventors of this invention and others.
The principle will be briefly described referring to FIG. 5.
Firstly, in the system where the active noise control can be applied, the primary noise is not supposed to be a white noise. If the application to a practical apparatus is considered, this supposition is natural.
At this time, the noise xj which is detected at the noise detecting microphone 201 and which is not the white noise can be regarded as the output of the filter W(z) (represented by xe2x80x9cWxe2x80x9d in Figure, and hereinafter will be represented similarly) which inputs a white noise Wj.
The feature of this apparatus lies in that before starting the active noise control, a filter Wxe2x88x921(z) having an inverse characteristic to a noise generation filter W(z) is preliminarily formed by a whitening circuit 310 shown in the upper part of FIG. 5.
This whitening circuit 310 can be formed by using, for example, a linear prediction method common in a voice analysis field. It can be said that the whitening circuit 310 has formed the inverse filter Wxe2x88x921(z) when the noise xj is whitened.
On the other hand, the output from the subtracter 204 after starting the active noise control becomes wjxc2x7W(z)/{1xe2x88x92D(z)A(z)}, where D(z) is a difference between a transfer function {circumflex over (B)}(z) of the feedback control filter 210 and a transfer function B(z) of the feedback path (feedback path within the duct 200 from the loud speaker 203 to the microphone 201), and A(z) is a transfer function of the noise control filter 220.
Accordingly, the signal outputted as a result that the inverse filter Wxe2x88x921(z) by the whitening circuit 310 is operated on the output of the subtracter 204 assumes an output in which a white noise wj is applied to the system whose transfer function is W(z)Wxe2x88x921(z)/{1xe2x88x92D(z)A(z)}, so that it is expressed by wjxc2x7W(z)Wxe2x88x921(z)/{1xe2x88x92D(z)A(z)}.
Obviously, since the numerator W(z)Wxe2x88x921(z) represents a simple delay, the coefficient of the inverse filter formed by the inverse filter composing circuit 110 assumes {1xe2x88x92D(z)A(z)}, if the above-mentioned output of the whitening circuit 310 is similarly whitened by using the composing circuit 110.
Furthermore, if an inverse filter 320 which provides the transfer function as {1xe2x88x92D(z)A(z)} is combined with a subtracter 330, the transfer function is given by the following equation:
1xe2x88x92{1xe2x88x92D(z)A(z)}=D(z)A(z)xe2x80x83xe2x80x83Eq.(19)
Accordingly, if this transfer function is made an unknown system function and the system identification circuit is formed by connecting the cascade connection of a copied noise control filter 360 formed by copying the coefficient of the noise control filter 220 and the adaptive filter 150 to the unknown system in parallel, the adaptive filter 150 at the time when the output of a subtracter 151 becomes the minimum is to provide a transfer function approximated to the above-mentioned transfer function D(z), since the transfer function of the copied noise control filter 360 is A(z) as mentioned above.
Namely, if the coefficient of the adaptive filter 150 is added to that of the feedback control filter 210 to be updated, the gain of a closed circuit formed by the feedback path is to be suppressed small.
However, in the apparatus mentioned in the Japanese Patent Application No.9-239776 (Japanese Patent Publication Laid-open No.11-85165) as mentioned above, that xe2x80x9cit is necessary that the inverse filter Wxe2x88x921(z) of the filter W(z) which generates the noise xj is formed before starting the active noise controlxe2x80x9d makes an issue.
Obviously, if the characteristic of the noise xj can change during the active noise control, the inverse filter composing circuit 110 does not compose the transfer function {1xe2x88x92D(z)A(z)}, and can not be applied to the system where the characteristic of the noise changes during the active noise control.
Therefore, in the present invention [2], the noise xj detected at the noise detecting microphone 201 is assumed to be the output of the filter W(z) for the white noise wj, in the same way as the present invention [1], while the process of estimating the inverse filter Wxe2x88x921(z) before starting the active noise control is not performed. Accordingly, the whitening circuit 310 in FIG. 5 is removed from the schematic diagram of the present invention in FIG. 4.
In the present invention, the same supposition as the linear prediction analysis of the voice, i.e. the process of generating the noise xj is supposed to be described by an all-pole model 1/{1xe2x88x92P(z)}. At this time, the output x(z) of the subtracter 204 obtained during the active noise control is as follows:                               X          ⁡                      (            z            )                          =                              1                                          {                                  1                  -                                      P                    ⁡                                          (                      z                      )                                                                      }                            ⁢                              {                                  1                  -                                                            D                      ⁡                                              (                        z                        )                                                              ⁢                                          A                      ⁡                                              (                        z                        )                                                                                            }                                              =                      1                          1              -                              P                ⁡                                  (                  z                  )                                            -                                                D                  ⁡                                      (                    z                    )                                                  ⁢                                  A                  ⁡                                      (                    z                    )                                                              +                                                P                  ⁡                                      (                    z                    )                                                  ⁢                                  D                  ⁡                                      (                    z                    )                                                  ⁢                                  A                  ⁡                                      (                    z                    )                                                                                                          Eq        .                  (          20          )                    
If this output is provided to the input of the inverse filter composing circuit 110 in FIG. 4 and the inverse filter Xxe2x88x921(z) is formed within the inverse filter composing circuit 110 by applying thereto e.g. the linear prediction analysis method, the coefficient of the inverse filter whose transfer function is
Xxe2x88x921(z)=1xe2x88x92P(z)xe2x88x92D(z)A(z)+P(z)D(z)A(z)xe2x80x83xe2x80x83Eq.(21)
can be obtained.
In this inverse filter Xxe2x88x921(z), two unknown transfer functions P(z) and D(z) are included. In order to eliminate one of the unknown number P(z) and extract the other unknown number D(z) which is the object of the present invention, two independent equations (simultaneous equations) are required.
In the present invention, as a method for obtaining the two independent equations, a method is adopted for forming two transfer functions X1xe2x88x921(z) and X2xe2x88x921(z), which can be realized by providing two pairs of independent coefficients to the noise control filter 220 or the feedback control filter 210 (see FIG. 30) at the inverse filter composing circuit 110.
(2-1) Case of Providing Two Pairs of Fixed Coefficients to Noise Control Filter 220:
This case takes advantage of the coefficients of the noise control filter 220 being arbitrarily set if the decrease of the noise reduction quantity is allowed. Namely, if the coefficients of noise control filter 220 is modified with a time interval to the extent that the noise reduction quantity does not excessively lower below an allowable range so that two pairs of coefficients forming two different transfer functions A1(z) and A2(z) of the noise control filter 220 are provided, the inverse filter composing circuit 110 composes the inverse filters whose transfer functions are respectively given by the following equations for each pair of the coefficients:
X1xe2x88x921(z)=1xe2x88x92P(z)xe2x88x92D(z)A1(z)+P(z)D(z)A1(z)xe2x80x83xe2x80x83Eq.(22)
X2xe2x88x921(z)=1xe2x88x92P(z)xe2x88x92D(z)A2(z)+P(z)D(z)A2(z)xe2x80x83xe2x80x83Eq.(23)
In this case, the transfer functions X1xe2x88x921(z) and X2xe2x88x921(z) are obtained, if the transfer functions A1(z) and A2(z) are respectively determined.
If the both equations are transformed as                               P          ⁡                      (            z            )                          =                              1            -                                          X                1                                  -                  1                                            ⁡                              (                z                )                                      -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  1                                ⁡                                  (                  z                  )                                                                          1            -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  1                                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          24          )                                                  P          ⁡                      (            z            )                          =                              1            -                                          X                2                                  -                  1                                            ⁡                              (                z                )                                      -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  2                                ⁡                                  (                  z                  )                                                                          1            -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  2                                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          25          )                    
and the unknown number P(z) is eliminated, and the equation is arranged for the other unknown number D(z), the following equation can be obtained:                               D          ⁡                      (            z            )                          =                                                            X                2                                  -                  1                                            ⁡                              (                z                )                                      -                                          X                1                                  -                  1                                            ⁡                              (                z                )                                                                                                          A                  1                                ⁡                                  (                  z                  )                                            ⁢                                                X                  2                                      -                    1                                                  ⁡                                  (                  z                  )                                                      -                                                            A                  2                                ⁡                                  (                  z                  )                                            ⁢                                                X                  1                                      -                    1                                                  ⁡                                  (                  z                  )                                                                                        Eq        .                  (          26          )                    
The right side of Eq.(26) is all composed of known transfer functions, and the left side D(z) is, as mentioned above, the difference between the transfer function {circumflex over (B)}(z) of the feedback control filter 210 and the transfer function B(z) of the feedback path. Therefore, if the filter coefficient composing the transfer function of Eq.(26) is added to the coefficient of the feedback control filter 210, the transfer function B(z) of the feedback path can be obtained, whereby the object of the present invention can be achieved.
(2-2) Case of Providing Two Pairs of Fixed Coefficients to Feedback Control Filter 210:
The coefficients of the feedback control filter 210 can also be set arbitrarily, if the increase of the feedback quantity is allowed. Namely, the coefficients of the feedback control filter 210 is modified to the extent that the howling does not occur as follows:
D1(z)=B(z)xe2x88x92{circumflex over (B)}1(z)xe2x80x83xe2x80x83Eq.(27)
D2(z)=B(z)xe2x88x92{circumflex over (B)}2(z)xe2x80x83xe2x80x83Eq.(28)
By these equations, the inverse filter composing circuit 110 composes the inverse filters whose transfer functions are as follows:
X1xe2x88x921(z)=1xe2x88x92P(z)xe2x88x92{B(z)xe2x88x92{circumflex over (B)}1(z)}A(z)+P(z){B(z)xe2x88x92{circumflex over (B)}1(z)}A(z)xe2x80x83xe2x80x83Eq.(29)
X2xe2x88x921(z)=1xe2x88x92P(z)xe2x88x92{B(z)xe2x88x92{circumflex over (B)}2(z)}A(z)+P(z){B(z)xe2x88x92{circumflex over (B)}2(z)}A(z)xe2x80x83xe2x80x83Eq.(30)
If both equations are arranged to eliminate the unknown number P(z) as follows:                               P          ⁡                      (            z            )                          =                              1            -                                          X                1                                  -                  1                                            ⁡                              (                z                )                                      -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            1                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                              A                ⁡                                  (                  z                  )                                                                          1            -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            1                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                              A                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          31          )                                                  P          ⁡                      (            z            )                          =                              1            -                                          X                2                                  -                  1                                            ⁡                              (                z                )                                      -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            2                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                              A                ⁡                                  (                  z                  )                                                                          1            -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            2                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                              A                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          32          )                    
and both are assumed equal, the following equation can be obtained:
[1xe2x88x92X2xe2x88x921(z)xe2x88x92{B(z)xe2x88x92{circumflex over (B)}2(z)}A(z)xe2x88x92][1xe2x88x92{B(z)xe2x88x92{circumflex over (B)}1(z)}A(z)]=
[1xe2x88x92X1xe2x88x921(z)xe2x88x92{B(z)xe2x88x92{circumflex over (B)}1(z)}A(z)xe2x88x92][1xe2x88x92{B(z)xe2x88x92{circumflex over (B)}2(z)}A(z)]xe2x80x83xe2x80x83Eq.(33)
If this equation is arranged for the other unknown number B(z), the following equation can be obtained:                               B          ⁡                      (            z            )                          =                                                            X                2                                  -                  1                                            ⁡                              (                z                )                                      -                                          X                1                                  -                  1                                            ⁡                              (                z                )                                      +                                          A                ⁡                                  (                  z                  )                                            ⁢                              {                                                                                                                              B                          ^                                                1                                            ⁡                                              (                        z                        )                                                              ⁢                                                                  X                        2                                                  -                          1                                                                    ⁡                                              (                        z                        )                                                                              -                                                                                                              B                          ^                                                2                                            ⁡                                              (                        z                        )                                                              ⁢                                                                  X                        1                                                  -                          1                                                                    ⁡                                              (                        z                        )                                                                                            }                                                                        A              ⁡                              (                z                )                                      ⁢                          {                                                                    X                    2                                          -                      1                                                        ⁡                                      (                    z                    )                                                  -                                                      X                    1                                          -                      1                                                        ⁡                                      (                    z                    )                                                              }                                                          Eq        .                  (          34          )                    
This B(z) is a transfer function of the feedback path as mentioned above, and all of the transfer functions on the right side are known. Accordingly, if the filter coefficient forming the transfer function B(z) is reset to the feedback control filter 210, the response of the feedback path in the duct 200 is canceled, so that the gain of the closed circuit is decreased.
(2-3) Calculation of Coefficient by System Identification Circuit 120:
The circuit for calculating the filter coefficient forming Eq.(26) or Eq.(34) is hereby required. In the present invention, the calculation is performed by using the technique of the system identification.
Firstly, if the adaptive filter 150 whose transfer function is supposed to be d(z) is introduced to update the coefficient of the adaptive filter 150 in order that the difference between the output of the first filter 130 having the numerator of Eq.(26) as the transfer function, as shown in FIG. 4, and the output of the cascade connection of the second filter 140 and the adaptive filter 150 having the denominator of Eq.(26) as the transfer function may become the minimum, the cascade connection of the filters 140 and 150 are approximated to the same numerator (filter 130) upon the convergence of the coefficient of the adaptive filter 150, so that the numerator is equal to [A1(z)X2xe2x88x921(z)xe2x88x92A2(z)X1xe2x88x921(z)]D(z) for Eq.(26).
Namely, after the convergence, the coefficient of the adaptive filter 150 is to provide the transfer function d(z) approximated to D(z).
Accordingly, if the adaptive filter 150 and the feedback control filter 210 are similarly formed, by adding the coefficient of the adaptive filter 150 to that of the feedback control filter 210 the coefficient can be replaced by the coefficient which decreases the gain of the closed circuit.
This procedure is similarly applied to the method (by Eq.(34)) of performing the update by providing two pairs of fixed coefficients to the feedback control filter 210. The coefficients forming the transfer functions of the numerator and the denominator of Eq.(34) have only to be set in the first and the second filter 130 and 140 in FIG. 4.
It is to be noted that the above-mentioned system identification circuit can be transformed as follows:
To form the simultaneous equations by using a transfer function provided by the inverse filter composing circuit, from which a constant 1 is removed.
To form the simultaneous equations by setting the two pairs of fixed coefficients of the noise control filter or the feedback control filter to different taps upon the activation of the apparatus.
To set the two pairs of fixed coefficients of the noise control filter or the feedback control filter with a time interval.
To use coefficients obtained upon the last activation for the two pairs of fixed coefficients of the noise control filter or the feedback control filter upon the activation of the apparatus.
Not to update the coefficient of the feedback control filter when the gain of the adaptive filter becomes equal to or less than a fixed value upon a coefficient update performed by providing the two pairs of fixed coefficients to the noise control filter.
FIG. 6 shows a principle arrangement of an active noise control apparatus of a feedback type according to the present invention [3]. An inverse filter composing circuit 110 is one which forms a filter having a characteristic including a transfer function opposite to a closed circuit starting from the noise control filter 220 and returning to the noise control filter 220 again through both (parallel circuit) of the feedback path and the feedback control filter 210, the transfer function expressing a generation process of the primary noise.
A system identification circuit 120 is one for providing two pairs of different fixed coefficients either to the feedback control filter 210 or the noise control filter 220 and for identifying the transfer function of the feedback path by updating a coefficient of an adaptive filter 123 in order that a difference becomes a minimum between an output of a first filter 121 forming a numerator of a solution obtained by eliminating the transfer function component expressing the generation process of the primary noise, from simultaneous equations based on two transfer functions of an inverse filter formed within the inverse filter composing circuit 110 for the two pairs of coefficients and an output of the adaptive filter 123 connected to a second filter 122 in cascade forming a denominator of the solution.
Also, the system identification circuit 120 is repeatedly used for calculating the coefficient of the noise control filter 220 optimally canceling the primary noise, makes a numerator of a ratio of the transfer function expressing the generation process of the primary noise obtained from the simultaneous equations and the transfer function of the feedback path, the first filter 121, makes a denominator the second filter 122, so that the coefficient of the noise control filter 220 which optimally cancels the primary noise is calculated for that of the adaptive filter 123 which minimizes the output of the subtracter 124.
The operation principle of the active noise control apparatus of the feedback type shown in FIG. 6 will now be described.
The noise canceled by the active noise control apparatus of the feedback type is limited to a correlation component of the noise wj. The generation process of the correlation component of the noise wj can be expressed as the all-pole model, and the noise W(z) can be expressed as the following equation with the white Gaussian noise being inputted:                               W          ⁡                      (            z            )                          =                  1                      1            -                          P              ⁡                              (                z                )                                                                        Eq        .                  xe2x80x83                ⁢                  (          35          )                    
When the synthesized noise gj successfully cancels the correlation component of this noise wj, and the output ej of the microphone 201 is whitened, the output E(z) of the microphone in FIG. 37 becomes xe2x80x9c1xe2x80x9d in the following equation:                                                                         E                ⁡                                  (                  z                  )                                            =                                                W                  ⁡                                      (                    z                    )                                                  ⁢                                  {                                      1                    -                                                                                            A                          ⁡                                                      (                            z                            )                                                                          ⁢                                                  B                          ⁡                                                      (                            z                            )                                                                                                                      1                        -                                                                              D                            ⁡                                                          (                              z                              )                                                                                ⁢                                                      A                            ⁡                                                          (                              z                              )                                                                                                                                                            }                                                                                                        =                                                1                                      1                    -                                          P                      ⁡                                              (                        z                        )                                                                                            ⁢                                  {                                      1                    -                                                                                            A                          ⁡                                                      (                            z                            )                                                                          ⁢                                                  B                          ⁡                                                      (                            z                            )                                                                                                                      1                        -                                                                              D                            ⁡                                                          (                              z                              )                                                                                ⁢                                                      A                            ⁡                                                          (                              z                              )                                                                                                                                                            }                                                                                        Eq        .                  (          36          )                    
If Eq.(36) is arranged by applying E(z)=1, the following equation can be obtained:                               P          ⁡                      (            z            )                          =                                            A              ⁡                              (                z                )                                      ⁢                          B              ⁡                              (                z                )                                                          1            -                                          D                ⁡                                  (                  z                  )                                            ⁢                              A                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          37          )                    
If Eq.(37) is arranged for the transfer function A(z) of the noise control filter 220, the following equation is obtained:                               A          ⁡                      (            z            )                          =                              P            ⁡                          (              z              )                                                          B              ⁡                              (                z                )                                      +                                          P                ⁡                                  (                  z                  )                                            ⁢                              D                ⁡                                  (                  z                  )                                                                                        Eq        .                  xe2x80x83                ⁢                  (          38          )                    
Therefore, it is seen that the noise becomes the minimum when the coefficient forming the transfer function A(z) is provided to the noise control filter 220.
It is to be noted that
xe2x80x83D(z)=B(z)xe2x88x92{circumflex over (B)}(z)xe2x80x83xe2x80x83Eq.(39)
Namely, in order to obtain the transfer function A(z), the transfer functions B(z) and P(z) have only to be obtained.
The signals which can be monitored by the active noise control apparatus of the feedback type are only the output ej of the microphone 201 and the output xj of the subtracter 211. According to the arrangement of FIG. 37, the output xj of the subtracter 211 can be obtained as                                                                         X                ⁡                                  (                  z                  )                                            =                                                W                  ⁡                                      (                    z                    )                                                                    1                  -                                                            D                      ⁡                                              (                        z                        )                                                              ⁢                                                                  A                        ^                                            ⁡                                              (                        z                        )                                                                                                                                                                    =                              1                                  1                  -                                      P                    ⁡                                          (                      z                      )                                                        -                                                            D                      ⁡                                              (                        z                        )                                                              ⁢                                                                  A                        ^                                            ⁡                                              (                        z                        )                                                                              +                                                            P                      ⁡                                              (                        z                        )                                                              ⁢                                          D                      ⁡                                              (                        z                        )                                                              ⁢                                                                  A                        ^                                            ⁡                                              (                        z                        )                                                                                                                                                    Eq        .                  (          40          )                    
by substituting the above Eq.(35) when the coefficient whose transfer function is Â(z) is set in the noise control filter 220.
In the present invention, the inverse filter Xxe2x88x921(z) can be obtained for the output X(z) by using the inverse filter composing circuit 110. For instance, when the inverse filter composing circuit 110 is applied to the output X(z) shown in FIG. 7, the coefficient whose transfer function is
S(z)=P(z)+D(z)Â(z)xe2x88x92P(z)D(z)Â(z)xe2x80x83xe2x80x83Eq.(41)
is set in a non-recursive filter 271 when the output of a subtracter 272 becomes the minimum.
In this transfer function S(z), the unknown numbers P(z) and D(z) (i.e. B(z)) forming Eq.(38) are included. In order to calculate two unknown numbers P(z) and D(z), the equation obtained as Eq.(41) is not enough, so that another equation is required.
As a method for obtaining the two equations, as shown in the present invention [2], the fact that an arbitrary fixed coefficient can be set in the noise control filter 220 or the feedback control filter 210 can be utilized.
Namely, when two pairs of independent fixed coefficients are provided to the noise control filter 220 or the feedback control filter 210, the inverse filter composing circuit 110 provides two transfer functions S1(z) and S2(z) to the two pairs of coefficients, with which two equations (simultaneous equations) can be obtained as follows:
(3-1) Case of Providing Two Pairs of Coefficients to Noise Control Filter 220:
It is assumed that a slight decline of the noise reduction quantity can be allowed. Namely, if the coefficient A(z) of the noise control filter 220 is modified to the extent of the noise reduction quantity being not deteriorated greatly, and two pairs of coefficients forming two different transfer functions A1(z) and A2(z) are provided, the inverse filter composing circuit 110 composes the non-recursive filter 271 whose transfer functions as follows for the two coefficients:
S1(z)=P(z)+D(z)A1(z)xe2x88x92P(z)D(z)A1(z)xe2x80x83xe2x80x83Eq.(42)
S2(z)=P(z)+D(z)A2(z)xe2x88x92P(z)D(z)A2(z)xe2x80x83xe2x80x83Eq.(43)
If both equations are transformed as                               P          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  1                                ⁡                                  (                  z                  )                                                                          1            -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  1                                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          44          )                                                  P          ⁡                      (            z            )                          =                                                            S                2                            ⁡                              (                z                )                                      -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  2                                ⁡                                  (                  z                  )                                                                          1            -                                          D                ⁡                                  (                  z                  )                                            ⁢                                                A                  2                                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          45          )                    
and one unknown number P(z) is eliminated, one of the two unknown numbers can be obtained as follows:                               D          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                                          S                2                            ⁡                              (                z                )                                                                                                          A                  1                                ⁡                                  (                  z                  )                                            ⁢                              {                                  1                  -                                                            S                      2                                        ⁡                                          (                      z                      )                                                                      }                                      -                                                            A                  2                                ⁡                                  (                  z                  )                                            ⁢                              {                                  1                  -                                                            S                      1                                        ⁡                                          (                      z                      )                                                                      }                                                                        Eq        .                  (          46          )                    
It is to be noted that the transfer functions S1(z) and S2(z) can be obtained if the transfer functions A1(z) and A2(z) are determined by using the non-recursive filter 271 of FIG. 7.
Accordingly, the right side of Eq.(46) is all composed of known transfer functions, so that it is seen that the difference D(z) between the transfer function B(z) of the feedback control filter 210 and the transfer function B(z) of the feedback path can be calculated.
As shown in FIG. 6, if the numerator of Eq.(46) is obtained by the first filter 121, the denominator of Eq.(46) is obtained by the second filter 122, and the coefficient of the adaptive filter 123 is updated in order that no difference from the subtracter 124 is found, the transfer function D(z) can be obtained.
Similarly, from Eqs.(42) and (43), the left unknown number P(z) can be solved. Namely, the unknown transfer function D(z) is arranged as                               D          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                          P              ⁡                              (                z                )                                                                                        A                1                            ⁡                              (                z                )                                      ⁢                          {                              1                -                                  P                  ⁡                                      (                    z                    )                                                              }                                                          Eq        .                  (          47          )                                                  D          ⁡                      (            z            )                          =                                                            S                2                            ⁡                              (                z                )                                      -                          P              ⁡                              (                z                )                                                                                        A                2                            ⁡                              (                z                )                                      ⁢                          {                              1                -                                  P                  ⁡                                      (                    z                    )                                                              }                                                          Eq        .                  (          48          )                    
and then both is assumed equal, so that the following equation can be obtained:                               P          ⁡                      (            z            )                          =                                                                              S                  2                                ⁡                                  (                  z                  )                                            ⁢                                                A                  1                                ⁡                                  (                  z                  )                                                      -                                                            S                  1                                ⁡                                  (                  z                  )                                            ⁢                                                A                  2                                ⁡                                  (                  z                  )                                                                                                        A                1                            ⁡                              (                z                )                                      -                                          A                2                            ⁡                              (                z                )                                                                        Eq        .                  (          49          )                    
Namely, the determined transfer function A(z) of the noise control filter 220 which optimally cancels the noise xj to be controlled can be obtained by substituting D(z) and P(z), which are obtained by calculating the above-mentioned Eqs.(46) and (49), as well as the present transfer function {circumflex over (B)}(z) of the feedback control filter 210 for the following equation:                               A          ⁡                      (            z            )                          =                              P            ⁡                          (              z              )                                                                          B                ^                            ⁡                              (                z                )                                      +                                          {                                  1                  +                                      P                    ⁡                                          (                      z                      )                                                                      }                            ⁢                              D                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          50          )                    
in which Eq.(39) is substituted for Eq.(38) to be arranged.
However, the transfer function of the feedback path (loud speaker 203xe2x86x92microphone 201) has improved its accuracy more than the present transfer function at this point is obtained as follows from Eq.(46):
xe2x80x83{tilde over (B)}(z)={circumflex over (B)}(z)+D(z)=B(z)xe2x80x83xe2x80x83Eq.(51)
Otherwise, a correction of making {tilde over (B)}(z) a new transfer function of the feedback path would be more natural.
Therefore, the transfer function of the feedback path is changed into {tilde over (B)}(z) of Eq.(51). At this time, since the transfer function A(z) of the noise control filter 220 which optimally cancels the noise xj to be controlled is approximated to D(z)=0 for the new transfer function {tilde over (B)}(z) of the feedback path, the transfer function A(z) can be calculated from the following equation by Eqs.(50) and (51):                               A          ⁡                      (            z            )                          =                              P            ⁡                          (              z              )                                                          B              ~                        ⁡                          (              z              )                                                          Eq        .                  (          52          )                    
By obtaining the numerator P(z) in Eq.(52) at the first filter 121 in FIG. 6 and the denominator {tilde over (B)}(z) at the second filter 122, the coefficient a(z) of the adaptive filter 123 is updated in order that the output of the subtracter 124 may become xe2x80x9c0xe2x80x9d, so that the transfer function A(z) can be obtained.
(3-2) Case of Providing Two Pairs of Coefficients to Feedback Control Filter 210:
In the same way as the case of the noise control filter 220, the coefficients of the noise control filter 210 can be arbitrarily set if the increase of the feedback quantity is temporarily allowed. Namely, the coefficients whose transfer function assumes Â(z) are provided to the noise control filter 220, and the coefficients is modified to the extent that the howling does not occur to the feedback control filter 210, so that the coefficients are set in order that the difference D(z) may become as follows:
D1(z)=B(z)xe2x88x92{circumflex over (B)}1(z)xe2x80x83xe2x80x83Eq.(53)
D2(z)=B(z)xe2x88x92{circumflex over (B)}2(z)xe2x80x83xe2x80x83Eq.(54)
By these equations, the inverse filter composing circuit 110 composes the non-recursive filter 271 whose transfer functions are respectively as follows:
S1(z)P(z)+{B(z)xe2x88x92{circumflex over (B)}1(z)}Â(z)xe2x88x92P(z){B(z)xe2x88x92{circumflex over (B)}1(z)}Â(z)xe2x80x83xe2x80x83Eq.(55)
S2(z)P(z)+{B(z)xe2x88x92{circumflex over (B)}2(z)}Â(z)xe2x88x92P(z){B(z)xe2x88x92{circumflex over (B)}2(z)}Â(z)xe2x80x83xe2x80x83Eq.(56)
In order to eliminate the unknown number P(z), both equations are arranged as follows:                               P          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            1                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                                                          1            -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            1                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          57          )                                                  P          ⁡                      (            z            )                          =                                                            S                2                            ⁡                              (                z                )                                      -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            2                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                                                          1            -                                          {                                                      B                    ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            2                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                                                                        Eq        .                  (          58          )                    
If both are assumed equal, and are arranged for the other unknown number B(z), the following equation can be obtained:                               B          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                                          S                2                            ⁡                              (                z                )                                      +                                                            A                  ^                                ⁡                                  (                  z                  )                                            ⁢                              {                                                                                                    B                        ^                                            1                                        ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            2                                        ⁡                                          (                      z                      )                                                                      }                                      +                                                            A                  ^                                ⁡                                  (                  z                  )                                            ⁢                              {                                                                                                    S                        1                                            ⁡                                              (                        z                        )                                                              ⁢                                                                                            B                          ^                                                2                                            ⁡                                              (                        z                        )                                                                              -                                                                                    S                        2                                            ⁡                                              (                        z                        )                                                              ⁢                                                                                            B                          ^                                                1                                            ⁡                                              (                        z                        )                                                                                            }                                                                                        A                ^                            ⁡                              (                z                )                                      ⁢                          {                                                                    S                    1                                    ⁡                                      (                    z                    )                                                  -                                                      S                    2                                    ⁡                                      (                    z                    )                                                              }                                                          Eq        .                  (          59          )                    
As for Eq.(59), in the same way as the case where the schematic arrangement of FIG. 6 is applied to Eq.(46) in the above (3-1), the first filter 121 can only be applied to the numerator and the second filter 122 to the denominator.
Furthermore, in order to obtain the other unknown number P(z), Eqs.(55) and (56) are arranged as follows:                               B          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                          P              ⁡                              (                z                )                                      +                                                                                B                    ^                                    1                                ⁡                                  (                  z                  )                                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                            ⁢                              {                                  1                  -                                      P                    ⁡                                          (                      z                      )                                                                      }                                                                                        A                ^                            ⁡                              (                z                )                                      ⁢                          {                              1                -                                  P                  ⁡                                      (                    z                    )                                                              }                                                          Eq        .                  (          60          )                                                  B          ⁡                      (            z            )                          =                                                            S                2                            ⁡                              (                z                )                                      -                          P              ⁡                              (                z                )                                      +                                                                                B                    ^                                    2                                ⁡                                  (                  z                  )                                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                            ⁢                              {                                  1                  -                                      P                    ⁡                                          (                      z                      )                                                                      }                                                                                        A                ^                            ⁡                              (                z                )                                      ⁢                          {                              1                -                                  P                  ⁡                                      (                    z                    )                                                              }                                                          Eq        .                  (          61          )                    
By assuming that both are equal, the following equation can be obtained:                               P          ⁡                      (            z            )                          =                                                            S                1                            ⁡                              (                z                )                                      -                                          S                2                            ⁡                              (                z                )                                      +                                          {                                                                                                    B                        ^                                            1                                        ⁡                                          (                      z                      )                                                        -                                                                                    B                        ^                                            2                                        ⁡                                          (                      z                      )                                                                      }                            ⁢                                                A                  ^                                ⁡                                  (                  z                  )                                                                                        {                                                                                          B                      ^                                        2                                    ⁡                                      (                    z                    )                                                  -                                                                            B                      ^                                        1                                    ⁡                                      (                    z                    )                                                              }                        ⁢                                          A                ^                            ⁡                              (                z                )                                                                        Eq        .                  (          62          )                    
can be obtained.
When the coefficient of the feedback control filter 210 is not updated with Eq.(59) and the transfer function is maintained to e.g. {circumflex over (B)}1(z), the coefficient of the noise control filter 220 which cancels the noise xj to be controlled can be obtained by substituting B(z) and P(z) obtained with Eqs.(59) and (62) for the following equation:                                           A            ^                    ⁡                      (            z            )                          =                              P            ⁡                          (              z              )                                                                          {                                  1                  +                                      P                    ⁡                                          (                      z                      )                                                                      }                            ⁢                              B                ⁡                                  (                  z                  )                                                      -                                                            B                  ^                                1                            ⁡                              (                z                )                                                                        Eq        .                  (          63          )                    
in which Eq.(53) is applied to Eq.(38) to be arranged. Also, when the transfer function {circumflex over (B)}2(z) of the feedback control filter 210 is maintained, the coefficient of the noise control filter 220 which cancels the noise xj to be controlled is calculated by using the following equation:                                           A            ^                    ⁡                      (            z            )                          =                              P            ⁡                          (              z              )                                                                          {                                  1                  +                                      P                    ⁡                                          (                      z                      )                                                                      }                            ⁢                              B                ⁡                                  (                  z                  )                                                      -                                                            B                  ^                                2                            ⁡                              (                z                )                                                                        Eq        .                  (          64          )                    
In addition, when the coefficient of the feedback control filter 210 is updated by using Eq.(59), it is approximated to D(z)=0 in the same way as the above (3-1). Therefore, by using the new transfer function {tilde over (B)}(z) of the feedback control filter 210 calculated from Eq.(59), the following equation can be calculated:                                           A            ^                    ⁡                      (            z            )                          =                              P            ⁡                          (              z              )                                                          B              ~                        ⁡                          (              z              )                                                          Eq        .                  (          65          )                    
Also in this case, like the above (3-1), the coefficients of the noise control filter can be obtained by applying the numerator of Eq.(65) to the first filter 121 and the denominator to the second filter 122.
It is to be noted that the above-mentioned system identification circuit 120 can be transformed as follows:
To form the simultaneous equations by using a transfer function provided by the inverse filter composing circuit, from which a constant 1 is removed.
To form the simultaneous equations by setting the two pairs of fixed coefficients of the noise control filter or the feedback control filter to different taps upon the activation of the apparatus.
To make the two pairs of coefficients, which are to be set, of the noise control filter or the feedback control filter two pairs of coefficient of the noise control filter or the feedback control filter both set with a time interval.
To make the two pairs of coefficients, which are to be set, of the noise control filter or the feedback control filter upon the activation of the apparatus coefficients obtained and stored upon the last activation.
Not to update the coefficient of the feedback control filter when the difference between a new and an old coefficient of the feedback control filter becomes equal to or less than a fixed value upon a coefficient update performed by providing the two pairs of coefficients to the feedback control filter.
To apply a transfer function corresponding to a coefficient used for the present coefficient update for the two pairs of coefficients, which are to be set, of the noise control filter or the feedback control filter and the transfer function of the inverse filter upon a subsequent coefficient update of the feedback control filter.